论文标题
关于不均匀的一对相关的评论
Remarks about inhomogeneous pair correlations
论文作者
论文摘要
给定一个无限子集$ \ Mathcal A \ subseteq \ Mathbb n $，让$ a $表示其最小的$ n $元素。关于典型的$α\在[0,1] $中，集合$αa\ pmod 1 \ subset [0,1] $在[0,1] $中的典型$α\中，有一个丰富而越来越多的文献。我们定义了对配对相关概念的不均匀概括，并考虑了相应的双重度量问题。通常的设置中的许多结果都可以延续到这个新环境。此外，双重指标使我们能够建立一些新的结果，这些结果在文献中缺少单一的指标类似物。
Given an infinite subset $\mathcal A \subseteq\mathbb N$, let $A$ denote its smallest $N$ elements. There is a rich and growing literature on the question of whether for typical $α\in[0,1]$, the pair correlations of the set $αA \pmod 1\subset [0,1]$ are asymptotically Poissonian as $N$ increases. We define an inhomogeneous generalization of the concept of pair correlation, and we consider the corresponding doubly metric question. Many of the results from the usual setting carry over to this new setting. Moreover, the double metricity allows us to establish some new results whose singly metric analogues are missing from the literature.
